Browsing Matematisk institutt by Author "Karlsen, Kenneth H."
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Bendahmane, Mostafa; Karlsen, Kenneth H. (Research report / Forskningsrapport, 2005)We prove wellposedness (existence and uniqueness) results for aÊ class of degenerate reactiondiffusion systems. A prototype system belongingÊ to this class is provided by the bidomain model, which is frequently used toÊ ...

ANISOTROPIC NONLINEAR ELLIPTIC SYSTEMS WITH MEASURE DATA AND ANISOTROPIC HARMONIC MAPS INTO SPHERES Bendahmane, Mostafa; Karlsen, Kenneth H. (Research report / Forskningsrapport, 2004)We prove existence results for distributional solutions of anisotropic nonlinear elliptic systems with a measure valued righthand side. The functional setting involves anisotropic Sobolev spaces as well as weak Lebesgue ...

Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. (Research report / Forskningsrapport, 2004)The wear of steel balls in continuously operated grinding mills, used in mineral processing to comminute metalliferous rocks, can be described by a simple population balance model. This model gives rise to a scalar transport ...

Jakobsen, Espen R.; Karlsen, Kenneth H. (Research report / Forskningsrapport, 2004)We present a general framework for deriving continuous dependence estimates for, possibly polynomially growing, viscosity solutions of fully nonlinear degenerate parabolic integroPDEs. We use this framework to provide ...

Karlsen, Kenneth H.; Karper, Trygve K. (Research report / Forskningsrapport, 2009)We propose and analyze a finite element method for a semistationary Stokes system modeling compressible fluid flow subject to a Navierslip boundary condition. The velocity (momentum) equation is approximated by a mixed ...

Karlsen, Kenneth H.; Mishra, Siddhartha; Risebro, Nils Henrik (Research report / Forskningsrapport, 2006)We consider nonstrictly hyperbolic systems of conservation laws in triangular form, which arise in applications like threephase flows in porous media. We device simple and efficient finite volume schemes of Godunov type ...

Karlsen, Kenneth H.; Towers, John D. (Research report / Forskningsrapport, 2004)We give the first convergence proof for the LaxFriedrichs finite difference scheme for nonconvex genuinely nonlinear scalar conservation laws of the form $$ u_t+f(k(x,t),u)_x=0, $$ where the coefficient $k(x,t)$ is ...

Jakobsen, Espen R.; Karlsen, Kenneth H. (Research report / Forskningsrapport, 2004)We study a semidiscrete splitting method for computing approximate viscosity solutions of the initial value problem for a class of nonlinear degenerate parabolic equations with source terms. It is fairly standard to prove ...

Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils Henrik (Research report / Forskningsrapport, 2005)

Coclite, Giuseppe M.; Karlsen, Kenneth H.; Risebro, Nils Henrik (Research report / Forskningsrapport, 2006)We suggest a finite dfference scheme for the CamassaHolm equation that can handle general H1 initial data. The form of the difference scheme is judiciously chosen to ensure that it satisfies a total energy inequality. We ...

Karlsen, Kenneth H.; Karper, Trygve K. (Research report / Forskningsrapport, 2009)We propose a nonconforming finite element method for isentropic viscous gas flow in situations where convective effects may be neglected. We approximate the continuity equation by a piecewise constant discontinuous Galerkin ...

Jakobsen, Espen R.; Karlsen, Kenneth H.; La Chioma, Claudia (Research report / Forskningsrapport, 2005)We derive error estimates for approximate (viscosity) solutions of Bellman equations associated to controlled jumpdiffusion processes, which are fully nonlinear integropartial differential equations. Two main results are ...

Biswas, Imran H.; Jakobsen, Espen R.; Karlsen, Kenneth H. (Research report / Forskningsrapport, 2006)We derive error estimates for certain approximate solutions of Bellman equations associated to a class of controlled jumpdiffusion (Lévy) processes. These Bellman equations are fully nonlinear degenerate integroPDEs ...

Biswas, Imran H.; Jakobsen, Espen R.; Karlsen, Kenneth H. (Research report / Forskningsrapport, 2007)We derive error estimates for finite differencequadrature schemes approximating viscosity solutions of nonlinear degenerate parabolic integroPDEs with variable diffusion coefficients. The relevant equations can be viewed ...

Berre, Inga; Karlsen, Kenneth H.; Lie, K.A.; Natvig, Bent (Research report / Forskningsrapport, 2003)We continue the work that was initiated in [7] on a fast marchinglike method for simulating twophase incompressible immiscible flow of water and oil in a porous medium. The purpose ot the present paper is threefold: (1) ...

Karlsen, Kenneth H.; Risebro, Nils Henrik; Towers, John D. (Research report / Forskningsrapport, 2003)We propose and prove convergence of a front tracking method for scalar conservation laws with source term. The method is based on writing the single conservation law as a 2x2 quasilinear system without a source term, and ...

Coclite, Giuseppe M.; Holden, Helge; Karlsen, Kenneth H. (Research report / Forskningsrapport, 2004)We consider a generalized hyperelasticrod wave equation (or generalized CamassaHolm equation) describing nonlinear dispersive waves in compressible hyperelastic rods. We establish existence of a strongly continuous ...

Bendahmane, Mostafa; Coclite, Giuseppe M.; Karlsen, Kenneth H. (Research report / Forskningsrapport, 2005)We consider a weakly dissipative hyperelasticrod wave equation (or weakly dissipative CamassaHolm equation) describing nonlinear dispersive dissipative waves in compressible hyperelastic rods. By fixed a smooth solution, ...

Karlsen, Kenneth H.; Mishra, Siddhartha; Risebro, Nils Henrik (Research report / Forskningsrapport, 2006)We present a wellbalanced, large time stepping method for conservation laws with source terms. The numerical method is based on a local reformulation of the balance law as a conservation law with a discontinuous flux ...

Karlsen, Kenneth H.; Risebro, Nils Henrik; Towers, John D. (Research report / Forskningsrapport, 2003)We propose a Kruzkovtype entropy condition for nonlinear degenerate parabolic equations with discointinuous coefficients. We establish L1 stability, and thus uniqueness, for weak solutions satisfying the entropy condition, ...